I passed the entrance exam for the university of my first-choice but the major is my second-choice of the same school.
I made it in to the university of my first-choice with the mojor of my second-choice.
"I passed the entrance exam for the university of my first-choice but the major is my second-choice of the same school. "
"pass the entrance exam" - 「入試に合格する」
"the university of my first-choice" - 「第一希望の大学」
"the major" - 「専攻」という意味です。
"I made it in to the university of my first-choice with the major of my second-choice."
「合格した」を"make it in"という表現にし、"with"を使うことで文章自体をかなり省いてキーポイントだけ伝わるようにしました。
I did get into my first-choice school, but the department I was accepted into was my second choice.
"I did get into my first-choice school"=「第一志望の学校には受かりました」
"but the department I was accepted into was"＝「でも、受かった学科は」
"my second choice"＝「第二希望でした」
("department"とは「学部」という意味なので、"major"＝「専攻」という単語も使えます）
ご参考になると良いです！
日本 
アメリカ合衆国 
